It is fairly easy to show that the triangles AFE,
DFE, BFD, and DEC are congruent using the fact that DE || BA, DF || AC, FE ||
BC, and D, E, and F are midpoints.
Thus the area of triangle ABC is 4 times
the area of triangle DEF.
Using my GSP
you can see that the triangle DEF is smaller in area for every other
interior point and thus the ratio is greater than 4 for all other interior